The work done by an ideal gas of $2 \text{ moles}$ in increasing its volume from $V$ to $2V$ at constant temperature $T$ is $W$. The work done by an ideal gas of $4 \text{ moles}$ in increasing its volume from $V$ to $8V$ at constant temperature $\frac{T}{2}$ is:

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressures of the gases in $A$ and $B$ are found to be $2\Delta P$ and $3\Delta P$ respectively. Then the relation between $m_{A}$ and $m_{B}$ is

The work done to increase the volume of $2$ moles of an ideal gas from $V$ to $2V$ at a constant temperature $T$ is $W$. The work to be done to increase the volume of $2$ moles of the same gas from $2V$ to $4V$ at the same constant temperature $T$ is:

The volume of an ideal gas is $1 \, L$ and its pressure is equal to $72 \, cm$ of mercury column. The volume of the gas is made $900 \, cm^3$ by compressing it isothermally. The increase in the pressure of the gas will be ...... $cm$ of mercury.

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is ${m_A}$ and that in $B$ is ${m_B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then:

When an ideal gas in a cylinder was compressed isothermally by a piston,the work done on the gas was found to be $1.5 \times 10^4 \ J$. During this process,about: